Unless you have no skirt around your crawl space rats and anything else can get under your house.
If you put poison out for them, you will get dead rats too. And if your dog or cat eats the dead rat, they too will become ill. Most rodent poison is a commonly used blood thinner and it does not go away just because the rodent dies.
As for the smell, removing the dead body will make removing the much easier and while you are there removing the rat, spray the area with OdorXit Concentrate diluted 1 to 30 parts with water and the odor will be gone for ever. This also works in attics with roof/fruit rats.
OdorXit Products at www.odorxit.com is the place to get stuff to remove odors.